concepts is much
greater than one would believe before making a study of the subject, for
the idea that our common numerals are universal is far from being correct.
It will be well, then, to think of the numerals that we still commonly call
Arabic, as only one of many systems in use just before the Christian era.
As it then existed the system was no better than many others, it was of
late origin, it contained no zero, it was cumbersome and little used, {2}
and it had no particular promise. Not until centuries later did the system
have any standing in the world of business and science; and had the place
value which now characterizes it, and which requires a zero, been worked
out in Greece, we might have been using Greek numerals to-day instead of
the ones with which we are familiar.

Of the first number forms that the world used this is not the place to
speak. Many of them are interesting, but none had much scientific value. In
Europe the invention of notation was generally assigned to the eastern
shores of the Mediterranean until the critical period of about a century
ago,--sometimes to the Hebrews, sometimes to the Egyptians, but more often
to the early trading Phoenicians.[1]

The idea that our common numerals are Arabic in origin is not an old one.
The mediaeval and Renaissance writers generally recognized them as Indian,
and many of them expressly stated that they were of Hindu origin.[2] {3}
Others argued that they were probably invented by the Chaldeans or the Jews
because they increased in value from right to left, an argument that would
apply quite as well to the Roman and Greek systems, or to any other. It
was, indeed, to the general idea of notation that many of these writers
referred, as is evident from the words of England's earliest arithmetical
textbook-maker, Robert Recorde (c. 1542): "In that thinge all men do agree,
that the Chaldays, whiche fyrste inuented thys arte, did set these figures
as thei set all their letters. for they wryte backwarde as you tearme it,
and so doo they reade. And that may appeare in all Hebrewe, Chaldaye and
Arabike bookes ... where as the Greekes, Latines, and all nations of
Europe, do wryte and reade from the lefte hand towarde the ryghte."[3]
Others, and {4} among them such influential writers as Tartaglia[4] in
Italy and Koebel[5] in Germany, asserted the Arabic origin of the numerals,
while still others left the matter undecided[6] or simply dismissed them as
"barbaric."[